ACC2 represents four domains of the global earth system: (i) physical climate system, (ii) carbon cycle system, (iii) atmospheric chemistry system, and (iv) economy system. The first three domains are described in the next paragraph and the last one is described in the paragraph that follows. We keep the model description succinct here, only describing the aspects most pertinent to our present analysis. The current model was developed from earlier simple climate models (68, 69) and produces an equivalent output with the one used in (23). The performance of the model (except for the economic module) was evaluated with those of other simple climate models under a set of common scenarios (70). The model is written by the General Algebraic Modeling System (GAMS) language.

The physical climate system is represented by an energy balance model coupled with a heat diffusion model (22, 71). Radiative forcing agents considered in the model include CO2, CH4, N2O, and SF6; 29 species of halocarbons, tropospheric, and stratospheric O3; and stratospheric water vapor. Aerosol forcing is separated by three terms: the direct effect of sulfate aerosols, the direct effect of black carbon and organic aerosols, and the indirect effects of all aerosols. The CH4 lifetime is influenced by OH, NOx, CO, and VOC. Note that each forcing term is calculated separately without any gas aggregation using metrics such as GWP100. The global carbon cycle is provided by a box model: four boxes for the coupled atmosphere-ocean and another four for the land. Saturation of ocean CO2 uptake under rising atmospheric CO2 concentrations is modeled through the thermodynamic equilibrium of carbonate species in the ocean (72, 73). The CO2 fertilization of the land biosphere is parameterized by a commonly used β factor. No climate-carbon feedbacks are assumed in our analysis; that is, carbon cycle processes are assumed to be insensitive to the temperature change. The equilibrium climate sensitivity is fixed at 3°C, within the 1.5° to 4.5°C range suggested by the IPCC AR5 (in the Thematic Focus Elements 6). Other uncertain parameters such as those related to aerosol forcing and CO2 fertilization are optimized on the basis of a Bayesian approach using historical observations such as global-mean temperature changes and atmospheric CO2 concentrations (74). The interdependencies among the parameter estimates are considered, including the one between the climate sensitivity and the aerosol forcing strength (75). The optimization is performed by using CONOPT3, a nonlinear optimization solver provided with GAMS.

The economy module is used to estimate the costs of mitigating CO2 (fossil fuel origin), CH4, and N2O emissions based on a first-order method using global MAC curves (38, 45) (fig. S2). The MAC curves are assumed time-invariant and given as a function of the abatement level (in percent) of the respective gas relative to an assumed baseline level [i.e., the International Institute for Applied Systems Analysis (IIASA) Greenhouse Gas Initiative (GGI) A2r baseline scenario (76)]. The fossil fuel CO2 MAC curve is based on the output of the Global Energy Transition (GET) model (45), which was simulated iteratively under different future trajectories of the carbon price. Although the carbon price for a given level of emission reductions should be time-dependent, we use a mathematical function to approximate the data collected from 2060 to 2100 and apply it as the MAC function throughout the period in our analysis. Limitations associated with the fixed MAC curve approach are partially but imperfectly mitigated by the constraints on the temporal changes in the abatement level to account for the technological change and socioeconomic inertia associated with emission abatement. Namely, the rate of change in the abatement level (i.e., first derivative) is kept below 4% per year for all three gases, implying a limit for the technological change; furthermore, the rate of abatement change (i.e., second derivative) is below 0.4% per year, mimicking socioeconomic inertia. These first- and second-derivative constraints limit the extent of the MAC curves that can be used in the near term. The implication of these constraints is that, if the abatement starts in 2020, the abatement level can reach up to 20% in 2030, 60% in 2040, and 100% in 2050 (i.e., zero emissions from fossil fuel CO2). These constraints allow larger changes in the abatement level than those found in the 450 parts per million (ppm) CO2-equivalent scenarios in the AR5 database [supplementary figures 12 to 14 of (23)]. The maximum abatement levels for CO2 (fossil fuel origin), CH4, and N2O are assumed at 112, 70, and 50%, respectively. The abatement potential for CO2 can exceed 100% primarily because the IAM, on which our CO2 MAC curve is based, considers bioenergy combined with carbon capture and storage as an option in the mitigation portfolio (45). Such deep mitigation could affect biodiversity and food security through land-use changes associated with large-scale negative emissions in a way that may not be acceptable in the real world (4951), especially if large-scale low-diversity forest plantations and bioenergy crops coupled to capture and storage are the negative emissions technologies being preferentially adopted in the mid- to late century. Other political and governance constraints, which can be also important in the real world, are not considered in our model. Our approach is kept simple and works under the assumption that CO2 and non-CO2 mitigation measures are interchangeable, which is partially true given the necessity to finance mitigation actions but may also break down for measures involving co-reduction of GHGs. Our MAC curve approach does not capture GHG abatement measures entailing net negative costs that have, however, not been implemented because of non-economic factors. The emissions of all other gases and pollutants including CO2 from land-use change are prescribed without cost calculations (i.e., GGI A2r 480 ppm CO2-equivalent stabilization). The discount rate is assumed at 4% by default. We analyze the pathway until 2200, going beyond the 2100 time frame commonly analyzed. The long time frame is required to capture overshoot pathways under which temperatures will not return to 2°C or lower during this century.

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